Write a biquadratic equation that has as roots the numbers $2$ and $2\sqrt{2}$

Question

I thought the answer would be: $$(x^2 - 4)(x^2 - 8) = 0$$ but it has $4$ roots the positive and negative values. Which is the correct answer?

Answer 1

If you take biquadratic as a synonym for quartic then any of these work:

$$(x-2)^3(x-2\sqrt{2}) \\ (x-2)^2(x-2\sqrt{2})^2 \\ (x-2)(x-2\sqrt{2})^3$$

But otherwise I don't see how to get only those two roots in a quartic equation without odd powers (the more common definition of biquadratic).

However, as N.F. Taussig points out, what you have is correct, as long as you don't care if there are other roots besides $2$ and $2\sqrt{2}$. Also, it satisfies the more common definition of what a biquadratic equation is.